Understanding the Use of Variable Notation in the DTFT

AI Thread Summary
The discussion clarifies the use of variable notation in the Discrete-Time Fourier Transform (DTFT), specifically the distinction between capital omega (Ω) and e^(jω). Ω represents continuous frequency, which is suitable for the DTFT, while e^(jω) emphasizes the evaluation of frequency response on the unit circle. The z-transform is also mentioned as a crucial tool in digital signal processing (DSP), covering the entire complex plane. This notation helps in understanding the relationship between frequency and the DTFT. Overall, the choice of notation enhances clarity in analyzing frequency responses.
Jammin_James
Messages
49
Reaction score
0
Can someone explain to me why sometimes I see the DTFT as functions of capital omegas or e^(jomega).

I'm failing to see the reason.
 
Engineering news on Phys.org
\Omega usually refers to continuous frequency, which is often appropriate for the DTFT. The z transform is also used heavily in DSP, and it covers the full complex plane. Use of exp(j\omega) makes it very clear that you are evaluating the frequency response (which is on the unit circle).
 

Thread 'Underwater piezoelectric sensor array receive sensitivity'

Hi all I have some confusion about piezoelectrical sensors combination. If i have three acoustic piezoelectrical sensors (with same receive sensitivity in dB ref V/1uPa) placed at specific distance, these sensors receive acoustic signal from a sound source placed at far field distance (Plane Wave) and from broadside. I receive output of these sensors through individual preamplifiers, add them through hardware like summer circuit adder or in software after digitization and in this way got an...
View full post »

Thread 'Following up on the recent thread about Earth Resistance measurements'

I have recently moved into a new (rather ancient) house and had a few trips of my Residual Current breaker. I dug out my old Socket tester which tell me the three pins are correct. But then the Red warning light tells me my socket(s) fail the loop test. I never had this before but my last house had an overhead supply with no Earth from the company. The tester said "get this checked" and the man said the (high but not ridiculous) earth resistance was acceptable. I stuck a new copper earth...
View full post »
Thread 'Beauty of old electrical and measuring things, etc.'

Thread 'Beauty of old electrical and measuring things, etc.'

Even as a kid, I saw beauty in old devices. That made me want to understand how they worked. I had lots of old things that I keep and now reviving. Old things need to work to see the beauty. Here's what I've done so far. Two views of the gadgets shelves and my small work space: Here's a close up look at the meters, gauges and other measuring things: This is what I think of as surface-mount electrical components and wiring. The components are very old and shows how...
View full post »

Similar threads

Understanding the Variables of the FT and DTFT: Intuition and Differences
Replies
1
Views
1K
Understanding the discrete time Fourier transformation
Replies
3
Views
2K
Is my understanding of the Nyquist theorem correct?
Replies
4
Views
2K
DFT vs. DTFT: Understanding the Difference
Replies
1
Views
4K
DTFT vs the spectrum of a sampled signal
Replies
2
Views
2K
DTFT question regarding a pair
Replies
2
Views
1K
Ideal Filter - Windowed - DTFT/Highpass
Replies
1
Views
2K
Can the DTFT of a Unit Step Function be Simplified for u(n) - u(n-L)?
Replies
4
Views
8K
I Making Sense of Notation Confusion in Statistical Digital Signal Processing
Replies
6
Views
2K
Solving for the DTFT of (0.8)^n u[n]
Replies
1
Views
6K

Hot Threads

Recent Insights

Back
Top